Question

A and B are independent events. The probability that both A and B occur is \(\frac{1}{20}\) and the probability that neither of them occurs is \(\frac{3}{5}\). The probability of occurrence of \(A\) is
(A) \(\frac{1}{2}\)
(B) \(\frac{1}{10}\)
(C) \(\frac{1}{4}\)
(D) \(\frac{1}{5}\)

Answer 1

Ans: (C,D)
Hint \(: P\left(A^{\prime} \cap B^{\prime}\right)=\frac{3}{5}\)
$$
\Rightarrow 1-P(A \cup B)=\frac{3}{5}
$$
$$
\begin{aligned}
&\Rightarrow P(A \cup B)=\frac{2}{5} \\
&\Rightarrow P(A)+P(B)-P(A) \cdot P(B)=\frac{2}{5} \\
&\Rightarrow P(A)+P(B)=\frac{9}{20} \text { and } P(A) \cdot P(B)=\frac{1}{20}
\end{aligned}
$$

Answer 2

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Answer 3

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